Possible combinations of 16 basics

[Theban_Legion]

I've been thinking about the possibilities of movement. Here is something that I found interesting.

I am going to try to find a restricted number of possible combinations of just a few of the basic movements.

Handstrikes:

Punch
Elbow
Backfist
Handsword
Spearhand or Finger strike
Ridgehand

KICKS:

Front kick
Side kick
Roundhouse kick
Back kick

STANCES:

Neutral bow
Forward bow
Reverse bow
Cat 45
Cat 90
Horse

I will only take into consideration strikes given in one direction. I will not yet consider simultaneous hand strikes or chicken kicks. I will not take into consideration target areas.

How many possible combinations are there for 6 Handstrikes, 4 Kicks, and 6 Stances?

This is what I've come up with (someone check this please):

16 permutations of 1, or 16 factoral= 2.092278989*10 to the 13th power
or 20,922,789,890,000 possible useful, unuseful, and useless combinations of these 16 basic movements. That is 20.9 trillion possibilities.

Let's round up to 21 trillion. If there are only three catagories of movement (useful, unuseful, and useless), then let's assume for the sake of brevity that they are equal thirds.
If only 1/3 of these movements are useful, then there are 7 trillion possible useful combinations of these 16 basics.

If only 1 in 10 of these movements are useful, then there are 2 trillion possible useful combinations of these 16 basics.

If only 1 in 100 of these movements are useful, then there are 200 billion possible useful combinations of these 16 basics.

If only 1 in 1000 of these movements are useful, then there are 20 billion possible useful combinations of these 16 basics.

Being that College Algebra has never been my strongest skill, I welcome any correction that can be verified. I understand that the stance changes and transitions would occur more frequently then recognized by this simple formula. I recognize that this does not take into consideration all of the possibilities; however, the result is an awesome 'mind cookie.'

We really could spend the rest of our lives studying the martial arts and never touch on all of the possibilities.


Note: it is more than possible that I have used the wrong method :) . I welcome any correction as long as said correction includes your corrected number of possible combinations of these 16 movements.

As always, all opinions and comments are welcome.

[Theban_Legion]

To Mrkoffee:

What, no corrections yet??? :eek:

I am anticipating Prof. H's response. Maybe in a couple of days.
20.9 trillion seems like a very high figure, but the factoral is correct. Perhaps we should have used a different method, eh?

I would like to expand this to include methods of delivery (whipping, hammering, thrusting) as well as nailing down the stances. Should we go through the system and find the average/mean # of stance changes per tech? Maybe there is a way to evalute the principals involved.
Also would like to include dimensional considerations.

Can we say 'geek?'

It might be nothing more than #'s, but it is still good to understand what the domain (and range :rolleyes: ) of martial movement is.

[administrator]

I am going to try to find a restricted number of possible combinations of just a few of the basic movements.
To determine possibilities, it is much more than the factorial function to be used. Using 16!, all of your techniques are determined to contain all 16 basics. There are many more ways to determine the combinations of movements. One is:
combination function nCk:
where n=the number of items to be ordered,
k=the number of things within the outcome combination

nCk = n!/((n-k)!*k!)

If your technique contains only 5 basics from your list of 16, then the possible number of combinations would be:
16!/((16-5)!*5!) = 4368 possible combinations

If it contained 7 basics the possible combinations would be only = 11440

You should then see the that the greater number of basics used yields greater possibilites, but not nearly in the astronomical numbers of having all possibilities to pick from.

So, if you like to play with these ideas, I suggest using a given list like you listed, and determine what restraints that you want to place on the technique and go from there. Working out such combinations is very important, as it keeps your imagination fresh and forces you to become engaged in your practice. I would, however, suggest this as a 'brainstorming game' to use every now and then, and not to get away from active training and skill development.

Keep up the good questions.

Kevin Lamkin
Site Administrator

[Theban_Legion]

To determine possibilities, it is much more than the factorial function to be used. Using 16!, all of your techniques are determined to contain all 16 basics. There are many more ways to determine the combinations of movements. One is:
combination function nCk:
where n=the number of items to be ordered,
k=the number of things within the outcome combination

nCk = n!/((n-k)!*k!)

If your technique contains only 5 basics from your list of 16, then the possible number of combinations would be:
16!/((16-5)!*5!) = 4368 possible combinations

If it contained 7 basics the possible combinations would be only = 11440

You should then see the that the greater number of basics used yields greater possibilites, but not nearly in the astronomical numbers of having all possibilities to pick from.
YES!! This is what we were looking for! Thank you.
My brother kept saying that there was something wrong with just using a factoral, but we couldn't quite figure what :) .

I think that the numbers of variations that we're looking at clearly show us how limited we would be if we never thought beyond the 250 technique curriculum.
It would be nearly impossible to train with every possible useful movement, so we must internalize the concepts that govern martial movement, yes?

[administrator]

... so we must internalize the concepts that govern martial movement, yes?You must internalize before anything can become externalized.

Kevin Lamkin
Site Administrator

[Dragon77]

The EFS addresses this very same issue. Eric Lamkin explain in a seminar last year that one of the greatest challenges he overcame while designing the system was how to simplify all the possible combinations of natural weapons (basics) to instantly know what combination would be effective. In doing this he even took into account all the possibilities of direction, angle, method of execution, intent, and even if it was an indirect attack (fake or feint)! He explained that the breakthrough came when he moved from a 2-dimensional matrix to a 3-dimensional matrix and he created a formula that anyone can use to create or analyze a combination of moves.

You will find this in the Defender Level Manual. There is a section in the Strategic Offensive Methods division entitled "Theory and Methodology of Attack, Defense, and Counter-Attack"

In this section, all strikes are placed in the matrices (shown iin the book) to show all the possible combinations. He uses a simplified shorthand/forumla to make reading it easier. there is also a formula you can use to create any effective combination.

I can't tell you how amazing it is! I was absolutely floored by its throughness and simplicity. And its not just something to read about to fill your head with knowledge; you actually use it in your training and you will reach a point in which it all comes naturally.

I highly recommend that you pick this up. It may have the answers you are looking for. It certainly opened my eyes to a whole new world.

D77

[Theban_Legion]

Awesome! Defender manual, eh? I'm certainly going to pick that one up! EFS sounds brilliant.